If I play Mind Control, does the target creature I take control of have 'summoning sickness"? I'm assuming it does because it 'hasen't been under my control since the beginning of my turn' is this correct? So unless it specifically states that it has haste such as Act of Treason it will not be able to attack that turn correct? Also, if I gain control of a target creature that was tapped, would it remain tapped unless specifically stated otherwise?

since you did not control the creature since the beginning of the most recent step it has summoning sickness, yes.it will also keep all its states it had before, unless stated otherwise (so it will remain tapped, facedown, flipped, etc.)